Design of a simple memcapacitors-based oscillator from Colpitts’ LC-tank circuit: mathematical analysis, numerical and analog simulations

In this paper, a simple memcapacitors-based oscillator, set up from the Colpitts' LC tank circuit is presented. The oscillator is designed by replacing the two normal capacitors of Colpitts’ tank circuit with two nonlinear memcapacitors. The new resulting nonlinear circuit consists of only three dynamic elements, including two memcapacitors blocks and an inductor. The model is described as a continuous-time three-dimensional autonomous system with cubic nonlinearities. The structure of the equilibrium points and the discrete symmetries of the model equations are discussed. One of the key contributions in this area is the introduction of a simple circuit presenting peculiar behaviors such as offset bossing and coexisting of multiple attractors. An appropriate electronic circuit (analog simulator) is proposed to investigate the dynamic behavior of the proposed system and prove its feasibility. The proposed oscillator enriches the literature on simple memcapacitor-based circuits with complex dynamic behavior.